Weekly Problem 19 - 2012

The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

Weekly Problem 21 - 2013

In how many ways can seven of the numbers 1-9 be chosen such that they add up to a multiple of 3?

Weekly Problem 45 - 2013

Which of the numbers shown is the product of exactly 3 distinct prime factors?

Weekly Problem 48 - 2013

What is the remainder when the number 743589×301647 is divided by 5?

Weekly Problem 49 - 2013

What is the value of 2000 + 1999 × 2000?

If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?

The numbers 72, 8, 24, 10, 5, 45, 36, 15 are grouped in pairs so that each pair has the same product. Which number is paired with 10?

The following sequence continues indefinitely... Which of these integers is a multiple of 81?

If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

How many pairs of numbers of the form x, 2x+1 are there in which both numbers are prime numbers less than 100?

Weekly Problem 1 - 2009

Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?

Weekly Problem 11 - 2009

How many of the numbers 1 to 20 are not the sum of two primes?

Weekly Problem 13 - 2009

How many zeros does 50! have at the end?

At a cinema a child's ticket costs £$4.20$ and an adult's ticket costs £$7.70$. How much did is cost this group of adults and children to see a film?

Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?

Weekly Problem 6 - 2010

Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?

Weekly Problem 7 - 2010

Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

Weekly Problem 17 - 2010

The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

Weekly Problem 22 - 2010

Can you form this 2010-digit number...

Weekly Problem 30 - 2010

Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.

Weekly Problem 38 - 2010

The product of four different positive integers is 100. What is the sum of these four integers?

Weekly Problem 48 - 2010

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

Weekly Problem 5 - 2011

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

Weekly Problem 7 - 2011

Roo wants to puts stickers on the cuboid he has made from little cubes. Will he have any stickers left over?

Weekly Problem 10 - 2011

Will this product give a perfect square?

Weekly Problem 25 - 2011

Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?

Weekly Problem 35 - 2011

You are given lots of clues about a number. Can you work out what it is?

Weekly Problem 5 - 2014

What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?

Weekly Problem 15 - 2014

How many three digit numbers formed with three different digits from 0, 1, 2, 3 and 5 are divisible by 6?

Weekly Problem 26 - 2014

Which of the given numbers are divisible by 6?

Weekly Problem 28 - 2014

What is the units digit of the given expression?

Weekly Problem 39 - 2014

A whole number less than 100 gives remainders of 2, 3 and 4 when divided by 3, 4 and 5. What is the remainder when it is divided by 7?

Weekly Problem 1 - 2015

If $p$ and $q$ are prime numbers greater than $3$ and $q=p+2$, prove that $pq+1$ is divisible by $36$.

Weekly Problem 4 - 2015

Given any positive integer n, Paul adds together the factors of n, apart from n itself. Which of the numbers 1, 3, 5, 7 and 9 can never be Paul's answer?

Weekly Problem 6 - 2015

Charlie doesn't want his new house number to be divisible by 3 or 5. How many choices of house does he have?

Weekly Problem 33 - 2015

How many integers $n$ are there for which $n$ and $n^3+3$ are both prime?

Weekly Problem 1 - 2016

What is the last-but-one digit of 99! ?

Weekly Problem 2 - 2016

How many tables of each type does Mark need at his birthday party?

Weekly Problem 3 - 2016

How many times has Simon's age changed from a square to a prime?

Weekly Problem 7 - 2016

What is the smallest number of pieces grandma should cut her cake into to guarentee each grandchild gets the same amount of cake and none is left over.

Weekly Problem 18 - 2016

The year 2010 is one in which the sum of the digits is a factor of the year itself. What is the next year that has the same property?

Weekly Problem 25 - 2016

A list is made of every digit that is the units digit of at least one prime number. How many digits appear in the list?

Weekly Problem 28 - 2016

Last week, Tom and Sophie bought some stamps for their collections. Each stamp Tom bought cost him £1.10, whilst Sophie paid 70p for each of her stamps. Between them they spent exactly £10. How many stamps did they buy in total?

Weekly Problem 32 - 2016

What is the smallest integer which has every digit a 3 or a 4 and is divisible by both 3 and 4?

Weekly Problem 36 - 2016

What percentage of the integers between 1 and 10,000 are square numbers?

Weekly Problem 42 - 2016

What is the remainder when 354972 is divided by 7?

Weekly Problem 51 - 2016

Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?

Weekly Problem 6 - 2017

In the multiplication table on the right, only some of the numbers have been given. What is the value of A+B+C+D+E?

Weekly Problem 8 - 2017

A pattern repeats every six symbols. What are the 100th and 101st symbols?

Weekly Problem 22 - 2017

Peter wrote a list of all the numbers that can be formed by changing one digit of the number 200. How many of Peter's numbers are prime?

Weekly Problem 26 - 2017

The angles in the triangle are shown in the diagram in terms of x and y. If x and y are positive integers, what is the value of x+y?

Weekly Problem 30 - 2017

The prime numbers p and q are the smallest primes that differ by 6. What is the value of p+q?

Weekly Problem 34 - 2017

An abundant number is a positive integer N such that the sum of the factors of N is larger than 2N. What is the smallest abundant number?

Weekly Problem 5 - 2017

Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?

Weekly Problem 13 - 2017

Anastasia thinks of a number. Each of her friends performs an operation on it. The total of these is a square number. What is the smallest number Anastasia could have thought of?

Weekly Problem 21 - 2017

Four cards have a number on one side and a phrase on the back. On each card, the number does not have the property described on the back. What do the four cards have on them?

Weekly Problem 35 - 2017

144 divided by n leaves a remainder of 11. 220 divided by n also leaves a remainder of 11. What is n?

Weekly Problem 47 - 2017

How many numbers do I need in a list to have two squares, two primes and two cubes?